Practice Problems on Gauss Divergence Theorem
P1. By using the Divergence theorem, evaluate where, = sin (πx) i + zy3 j + (z2 + 4x) k and S is the surface of the box with -1 ≤ x ≤ 2, 0 ≤ y ≤1 and 1 ≤ z ≤ 4. All the six sides are included in S.
P2. By using the Divergence theorem, evaluate where, = yx2 i + (x y – 3x5) j + (x – 6y) k and S is the surface of the sphere with radius of sphere is 5, y ≤ 0 and z ≤ 0. All the three surfaces of solid are included in S.
P3. By using Gauss Divergence Theorem, compute where, F = (x4 + 4y, 5y2 – cot x2 , xe3z) and 0 ≤ x ≤ 2, 1 ≤ y ≤ 5 and -1 ≤ z ≤ 1.
P4. By using Gauss Divergence Theorem, compute where, F = (x2 + y2 + z2, 5y3 – z4 , xz5e3y) and -1 ≤ x ≤ 3, 1 ≤ y ≤ 3 and -2 ≤ z ≤ 2.
Divergence Theorem
Divergence Theorem is one of the important theorems in Calculus. The divergence theorem relates the surface integral of the vector function to its divergence volume integral over a closed surface.
In this article, we will dive into the depth of the Divergence theorem including the divergence theorem statement, divergence theorem formula, Gauss Divergence theorem statement, Gauss Divergence theorem formula, and Gauss Divergence Theorem proof.
We will also go through some points on Gauss’s Divergence theorem vs Green’s theorem, solve some examples, and answer some FAQs related to the divergence theorem.
Table of Content
- What is Divergence Theorem?
- Divergence Theorem Formula
- Gauss Divergence Theorem
- Proof of Gauss Divergence Theorem
- Gauss’s Divergence Theorem vs. Green’s Theorem
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